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The spectral theory of transients (STT) formulated in Parts I and II of this paper is here applied to the evaluation of the source-excited pulsed response for a representative class of two-dimensional examples: 1) a dielectric half-space with planar interface, 2) a dielectric half-space with curved interface, and 3) an edge-terminated curved perfectly conducting sheet. These configurations give rise to a variety, of propagation and diffraction phenomena such as those caused by lateral waves, by caustic-forming multiple reflected fields, by edge diffraction with formation of shadow boundaries, and by combinations of these. The results are established by direct utilization of the general formulas in Parts I and II, with emphasis on the spectral features associated with the various wave types. Sketches of the corresponding waveforms elucidate the behavior of the observed signal response.